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From er...@apache.org
Subject svn commit: r1067216 - in /commons/proper/math/trunk/src: main/java/org/apache/commons/math/optimization/direct/CMAESOptimizer.java test/java/org/apache/commons/math/optimization/direct/CMAESOptimizerTest.java
Date Fri, 04 Feb 2011 16:36:08 GMT
Author: erans
Date: Fri Feb  4 16:36:08 2011
New Revision: 1067216

URL: http://svn.apache.org/viewvc?rev=1067216&view=rev
Log:
MATH-442
Original code provided by Dietmar Wolz.

Added:
    commons/proper/math/trunk/src/main/java/org/apache/commons/math/optimization/direct/CMAESOptimizer.java   (with props)
    commons/proper/math/trunk/src/test/java/org/apache/commons/math/optimization/direct/CMAESOptimizerTest.java   (with props)

Added: commons/proper/math/trunk/src/main/java/org/apache/commons/math/optimization/direct/CMAESOptimizer.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/optimization/direct/CMAESOptimizer.java?rev=1067216&view=auto
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/optimization/direct/CMAESOptimizer.java (added)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/optimization/direct/CMAESOptimizer.java Fri Feb  4 16:36:08 2011
@@ -0,0 +1,1316 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math.optimization.direct;
+
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.List;
+
+import org.apache.commons.math.analysis.MultivariateRealFunction;
+import org.apache.commons.math.exception.MultiDimensionMismatchException;
+import org.apache.commons.math.exception.NoDataException;
+import org.apache.commons.math.exception.NotPositiveException;
+import org.apache.commons.math.exception.OutOfRangeException;
+import org.apache.commons.math.exception.TooManyEvaluationsException;
+import org.apache.commons.math.linear.Array2DRowRealMatrix;
+import org.apache.commons.math.linear.EigenDecomposition;
+import org.apache.commons.math.linear.EigenDecompositionImpl;
+import org.apache.commons.math.linear.MatrixUtils;
+import org.apache.commons.math.linear.RealMatrix;
+import org.apache.commons.math.optimization.GoalType;
+import org.apache.commons.math.optimization.MultivariateRealOptimizer;
+import org.apache.commons.math.optimization.RealPointValuePair;
+import org.apache.commons.math.random.MersenneTwister;
+import org.apache.commons.math.random.RandomGenerator;
+
+/**
+ * CMA-ES algorithm. This code is translated and adapted from the Matlab version
+ * of this algorithm as implemented in module {@code cmaes.m} version 3.51.
+ *
+ * Implements the active Covariance Matrix Adaptation Evolution Strategy (CMA-ES)
+ * for non-linear, non-convex, non-smooth, global function minimization.
+ * The CMA-Evolution Strategy (CMA-ES) is a reliable stochastic optimization method
+ * which should be applied, if derivative based methods, e.g. quasi-Newton BFGS or
+ * conjugate gradient, fail due to a rugged search landscape (e.g. noise, local
+ * optima, outlier, etc.)  of the objective function. Like a
+ * quasi-Newton method the CMA-ES learns and applies a variable metric
+ * of the underlying search space. Unlike a quasi-Newton method the
+ * CMA-ES does neither estimate nor use gradients, making it considerably more
+ * reliable in terms of finding a good, or even close to optimal, solution, finally.
+ *
+ * <p>In general, on smooth objective functions the CMA-ES is roughly ten times
+ * slower than BFGS (counting objective function evaluations, no gradients provided).
+ * For up to <math>N=10</math> variables also the derivative-free simplex
+ * direct search method (Nelder and Mead) can be faster, but it is
+ * far less reliable than CMA-ES.</p>
+ *
+ * <p>The CMA-ES is particularly well suited for non-separable
+ * and/or badly conditioned problems.
+ * To observe the advantage of CMA compared to a conventional
+ * evolution strategy, it will usually take about <math>30 N</math> function
+ * evaluations. On difficult problems the complete
+ * optimization (a single run) is expected to take <em>roughly</em> between
+ * <math>30 N</math> and <math>300 N<sup>2</sup></math>
+ * function evaluations.</p>
+ *
+ * For more information, please refer to the following links:
+ * <ul>
+ *  <li><a href="http://www.lri.fr/~hansen/cmaes.m">Matlab code</a></li>
+ *  <li><a href="http://www.lri.fr/~hansen/cmaesintro.html">Introduction to CMA-ES</a></li>
+ *  <li><a href="http://en.wikipedia.org/wiki/CMA-ES">Wikipedia</a></li>
+ * </ul>
+ *
+ * @version $Revision$ $Date$
+ * @since 3.0
+ */
+
+public class CMAESOptimizer extends
+        BaseAbstractScalarOptimizer<MultivariateRealFunction> implements
+        MultivariateRealOptimizer {
+
+    /** Default value for {@link #checkFeasableCount}: {@value}. */
+    public static final int DEFAULT_CHECKFEASABLECOUNT = 0;
+    /** Default value for {@link #stopfitness}: {@value}. */
+    public static final double DEFAULT_STOPFITNESS = 0;
+    /** Default value for {@link #isActiveCMA}: {@value}. */
+    public static final boolean DEFAULT_ISACTIVECMA = true;
+    /** Default value for {@link #maxIterations}: {@value}. */
+    public static final int DEFAULT_MAXITERATIONS = 30000;
+    /** Default value for {@link #diagonalOnly}: {@value}. */
+    public static final int DEFAULT_DIAGONALONLY = 0;
+    /** Default value for {@link #random}. */
+    public static final RandomGenerator DEFAULT_RANDOMGENERATOR = new MersenneTwister();
+
+    // global search parameters
+    /**
+     * Population size, offspring number. The primary strategy parameter to play
+     * with, which can be increased from its default value. Increasing the
+     * population size improves global search properties in exchange to speed.
+     * Speed decreases, as a rule, at most linearely with increasing population
+     * size. It is advisable to begin with the default small population size.
+     */
+    private int lambda; // population size
+    /**
+     * Covariance update mechanism, default is active CMA. isActiveCMA = true
+     * turns on "active CMA" with a negative update of the covariance matrix and
+     * checks for positive definiteness. OPTS.CMA.active = 2 does not check for
+     * pos. def. and is numerically faster. Active CMA usually speeds up the
+     * adaptation.
+     */
+    private boolean isActiveCMA;
+    /**
+     * Determines how often a new random offspring is generated in case it is
+     * not feasible / beyond the defined limits, default is 0. Only relevant if
+     * boundaries != null.
+     */
+    private int checkFeasableCount;
+    /**
+     * Lower and upper boundaries of the objective variables. boundaries == null
+     * means no boundaries.
+     */
+    private double[][] boundaries;
+    /**
+     * Individual sigma values - initial search volume. inputSigma determines
+     * the initial coordinate wise standard deviations for the search. Setting
+     * SIGMA one third of the initial search region is appropriate.
+     */
+    private double[] inputSigma;
+    /** Number of objective variables/problem dimension */
+    private int dimension;
+    /**
+     * Defines the number of initial iterations, where the covariance matrix
+     * remains diagonal and the algorithm has internally linear time complexity.
+     * diagonalOnly = 1 means keeping the covariance matrix always diagonal and
+     * this setting also exhibits linear space complexity. This can be
+     * particularly useful for dimension > 100.
+     * @see <a href="http://hal.archives-ouvertes.fr/inria-00287367/en">A Simple Modification in CMA-ES</a> .
+     */
+    private int diagonalOnly = 0;
+    /** Number of objective variables/problem dimension */
+    private boolean isMinimize = true;
+    /** Indicates whether statistic data is collected. */
+    private boolean generateStatistics = false;
+
+    // termination criteria
+    /** Maximal number of iterations allowed. */
+    private int maxIterations;
+    /** Limit for fitness value. */
+    private double stopfitness;
+    /** Stop if x-changes larger stopTolUpX. */
+    private double stopTolUpX;
+    /** Stop if x-change smaller stopTolX. */
+    private double stopTolX;
+    /** Stop if fun-changes smaller stopTolFun. */
+    private double stopTolFun;
+    /** Stop if back fun-changes smaller stopTolHistFun. */
+    private double stopTolHistFun;
+
+    // selection strategy parameters
+    /** Number of parents/points for recombination. */
+    private int mu; //
+    /** log(mu + 0.5), stored for efficiency. */
+    private double logMu2;
+    /** Array for weighted recombination. */
+    private RealMatrix weights;
+    /** Variance-effectiveness of sum w_i x_i. */
+    private double mueff; //
+
+    // dynamic strategy parameters and constants
+    /** Overall standard deviation - search volume. */
+    private double sigma;
+    /** Cumulation constant. */
+    private double cc;
+    /** Cumulation constant for step-size. */
+    private double cs;
+    /** Damping for step-size. */
+    private double damps;
+    /** Learning rate for rank-one update. */
+    private double ccov1;
+    /** Learning rate for rank-mu update' */
+    private double ccovmu;
+    /** Expectation of ||N(0,I)|| == norm(randn(N,1)). */
+    private double chiN;
+    /** Learning rate for rank-one update - diagonalOnly */
+    private double ccov1Sep;
+    /** Learning rate for rank-mu update - diagonalOnly */
+    private double ccovmuSep;
+
+    // CMA internal values - updated each generation
+    /** Objective variables. */
+    private RealMatrix xmean;
+    /** Evolution path. */
+    private RealMatrix pc;
+    /** Evolution path for sigma. */
+    private RealMatrix ps;
+    /** Norm of ps, stored for efficiency. */
+    private double normps;
+    /** Coordinate system. */
+    private RealMatrix B;
+    /** Scaling. */
+    private RealMatrix D;
+    /** B*D, stored for efficiency. */
+    private RealMatrix BD;
+    /** Diagonal of sqrt(D), stored for efficiency. */
+    private RealMatrix diagD;
+    /** Covariance matrix. */
+    private RealMatrix C;
+    /** Diagonal of C, used for diagonalOnly. */
+    private RealMatrix diagC;
+    /** Number of iterations already performed. */
+    private int iterations;
+
+    /** History queue of best values. */
+    private double[] fitnessHistory;
+    /** Size of history queue of best values. */
+    private int historySize;
+
+    /** Random generator. */
+    private RandomGenerator random;
+
+    /** History of sigma values. */
+    private List<Double> statisticsSigmaHistory = new ArrayList<Double>();
+    /** History of mean matrix. */
+    private List<RealMatrix> statisticsMeanHistory = new ArrayList<RealMatrix>();
+    /** History of fitness values. */
+    private List<Double> statisticsFitnessHistory = new ArrayList<Double>();
+    /** History of D matrix. */
+    private List<RealMatrix> statisticsDHistory = new ArrayList<RealMatrix>();
+
+    /**
+     * Default constructor, uses default parameters
+     */
+    public CMAESOptimizer() {
+        this(0);
+    }
+
+    /**
+     * @param lambda
+     *            Population size.
+     */
+    public CMAESOptimizer(int lambda) {
+        this(lambda, null, null, DEFAULT_MAXITERATIONS, DEFAULT_STOPFITNESS,
+                DEFAULT_ISACTIVECMA, DEFAULT_DIAGONALONLY,
+                DEFAULT_CHECKFEASABLECOUNT, DEFAULT_RANDOMGENERATOR, false);
+    }
+
+    /**
+     * @param lambda
+     *            Population size.
+     * @param inputSigma
+     *            Initial search volume - sigma of offspring objective
+     *            variables.
+     * @param boundaries
+     *            Boundaries for objective variables.
+     */
+    public CMAESOptimizer(int lambda, double[] inputSigma,
+            double[][] boundaries) {
+        this(lambda, inputSigma, boundaries, DEFAULT_MAXITERATIONS, DEFAULT_STOPFITNESS,
+                DEFAULT_ISACTIVECMA, DEFAULT_DIAGONALONLY,
+                DEFAULT_CHECKFEASABLECOUNT, DEFAULT_RANDOMGENERATOR, false);
+    }
+
+    /**
+     * @param lambda
+     *            Population size.
+     * @param inputSigma
+     *            Initial search volume - sigma of offspring objective
+     *            variables.
+     * @param boundaries
+     *            Boundaries for objective variables.
+     * @param maxIterations
+     *            Maximal number of iterations.
+     * @param stopfitness
+     *            stop if objective function value < stopfitness.
+     * @param isActiveCMA
+     *            Chooses the covariance matrix update method.
+     * @param diagonalOnly
+     *            Number of initial iterations, where the covariance matrix
+     *            remains diagonal.
+     * @param checkFeasableCount
+     *            Determines how often new. random objective variables are
+     *            generated in case they are out of bounds.
+     * @param random
+     *            Used random generator.
+     * @param generateStatistics
+     *            Indicates whether statistic data is collected.
+     */
+    public CMAESOptimizer(int lambda, double[] inputSigma,
+            double[][] boundaries, int maxIterations, double stopfitness,
+            boolean isActiveCMA, int diagonalOnly, int checkFeasableCount,
+            RandomGenerator random, boolean generateStatistics) {
+        this.lambda = lambda;
+        this.inputSigma = inputSigma;
+        this.boundaries = boundaries;
+        this.maxIterations = maxIterations;
+        this.stopfitness = stopfitness;
+        this.isActiveCMA = isActiveCMA;
+        this.diagonalOnly = diagonalOnly;
+        this.checkFeasableCount = checkFeasableCount;
+        this.random = random;
+        this.generateStatistics = generateStatistics;
+    }
+
+    /**
+     * @return History of sigma values.
+     */
+    public List<Double> getStatisticsSigmaHistory() {
+        return statisticsSigmaHistory;
+    }
+
+    /**
+     * @return History of mean matrix.
+     */
+    public List<RealMatrix> getStatisticsMeanHistory() {
+        return statisticsMeanHistory;
+    }
+
+    /**
+     * @return History of fitness values.
+     */
+    public List<Double> getStatisticsFitnessHistory() {
+        return statisticsFitnessHistory;
+    }
+
+    /**
+     * @return History of D matrix.
+     */
+    public List<RealMatrix> getStatisticsDHistory() {
+        return statisticsDHistory;
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    protected RealPointValuePair doOptimize() {
+        checkParameters();
+         // -------------------- Initialization --------------------------------
+        isMinimize = getGoalType().equals(GoalType.MINIMIZE);
+        final FitnessFunction fitfun = new FitnessFunction(boundaries,
+                isMinimize);
+        final double[] guess = fitfun.encode(getStartPoint());
+        // number of objective variables/problem dimension
+        dimension = guess.length;
+        initializeCMA(guess);
+        iterations = 0;
+        double bestValue = fitfun.value(guess);
+        push(fitnessHistory, bestValue);
+        RealPointValuePair optimum = new RealPointValuePair(getStartPoint(),
+                isMinimize ? bestValue : -bestValue);
+        RealPointValuePair lastResult = null;
+
+        // -------------------- Generation Loop --------------------------------
+
+        generationLoop:
+            for (iterations = 1; iterations <= maxIterations; iterations++) {
+                // Generate and evaluate lambda offspring
+                RealMatrix arz = randn1(dimension, lambda);
+                RealMatrix arx = zeros(dimension, lambda);
+                double[] fitness = new double[lambda];
+                // generate random offspring
+                for (int k = 0; k < lambda; k++) {
+                    RealMatrix arxk = null;
+                    for (int i = 0; i < checkFeasableCount+1; i++) {
+                        if (diagonalOnly <= 0)
+                            arxk = xmean.add(BD.multiply(arz.getColumnMatrix(k))
+                                    .scalarMultiply(sigma)); // m + sig * Normal(0,C)
+                        else
+                            arxk = xmean.add(times(diagD,arz.getColumnMatrix(k))
+                                    .scalarMultiply(sigma));
+                        if (i >= checkFeasableCount || fitfun.isFeasible(arxk.getColumn(0)))
+                            break;
+                        // regenerate random arguments for row
+                        arz.setColumn(k, randn(dimension));
+                    }
+                    copyColumn(arxk, 0, arx, k);
+                    try {
+                        fitness[k] = fitfun.value(arx.getColumn(k)); // compute fitness
+                    } catch (TooManyEvaluationsException e) {
+                        break generationLoop;
+                    }
+                }
+                // Sort by fitness and compute weighted mean into xmean
+                int[] arindex = sortedIndices(fitness);
+                // Calculate new xmean, this is selection and recombination
+                RealMatrix xold = xmean; // for speed up of Eq. (2) and (3)
+                RealMatrix bestArx = selectColumns(arx,Arrays.copyOf(arindex, mu));
+                xmean = bestArx.multiply(weights);
+                RealMatrix bestArz = selectColumns(arz,Arrays.copyOf(arindex, mu));
+                RealMatrix zmean = bestArz.multiply(weights);
+                boolean hsig = updateEvolutionPaths(zmean, xold);
+                if (diagonalOnly <= 0)
+                    updateCovariance(hsig, bestArx, arz, arindex, xold);
+                else
+                    updateCovarianceDiagonalOnly(hsig, bestArz, xold);
+                // Adapt step size sigma - Eq. (5)
+                sigma *= Math.exp(Math.min(1.0,(normps/chiN - 1.)*cs/damps));
+                double bestFitness = fitness[arindex[0]];
+                double worstFitness = fitness[arindex[arindex.length-1]];
+                if (bestValue > bestFitness) {
+                    bestValue = bestFitness;
+                    lastResult = optimum;
+                    optimum = new RealPointValuePair(
+                            fitfun.decode(bestArx.getColumn(0)),
+                            isMinimize ? bestFitness : -bestFitness);
+                    if (getConvergenceChecker() != null && lastResult != null) {
+                        if (getConvergenceChecker().converged(
+                                iterations, optimum, lastResult))
+                            break generationLoop;
+                    }
+                }
+                // handle termination criteria
+                // Break, if fitness is good enough
+                if (stopfitness != 0) { // only if stopfitness is defined
+                    if (bestFitness < (isMinimize ? stopfitness : -stopfitness))
+                        break generationLoop;
+                }
+                double[] sqrtDiagC = sqrt(diagC).getColumn(0);
+                double[] pcCol = pc.getColumn(0);
+                for (int i = 0; i < dimension; i++) {
+                    if (sigma*(Math.max(Math.abs(pcCol[i]), sqrtDiagC[i])) > stopTolX)
+                        break;
+                    if (i >= dimension-1)
+                        break generationLoop;
+                }
+                for (int i = 0; i < dimension; i++)
+                    if (sigma*sqrtDiagC[i] > stopTolUpX)
+                        break generationLoop;
+                double historyBest = min(fitnessHistory);
+                double historyWorst = max(fitnessHistory);
+                if (iterations > 2 && Math.max(historyWorst, worstFitness) -
+                        Math.min(historyBest, bestFitness) < stopTolFun)
+                    break generationLoop;
+                if (iterations > fitnessHistory.length &&
+                        historyWorst-historyBest < stopTolHistFun)
+                    break generationLoop;
+                // condition number of the covariance matrix exceeds 1e14
+                if (max(diagD)/min(diagD) > 1e7)
+                    break generationLoop;
+                // user defined termination
+                if (getConvergenceChecker() != null) {
+                    RealPointValuePair current =
+                        new RealPointValuePair(bestArx.getColumn(0),
+                                isMinimize ? bestFitness : -bestFitness);
+                    if (lastResult != null &&
+                            getConvergenceChecker().converged(
+                                    iterations, current, lastResult))
+                        break generationLoop;
+                    lastResult = current;
+                }
+                // Adjust step size in case of equal function values (flat fitness)
+                if (bestValue == fitness[arindex[(int)(0.1+lambda/4.)]])
+                    sigma = sigma * Math.exp(0.2+cs/damps);
+                if (iterations > 2 && Math.max(historyWorst, bestFitness) -
+                        Math.min(historyBest, bestFitness) == 0)
+                    sigma = sigma * Math.exp(0.2+cs/damps);
+                // store best in history
+                push(fitnessHistory,bestFitness);
+                fitfun.setValueRange(worstFitness-bestFitness);
+                if (generateStatistics) {
+                    statisticsSigmaHistory.add(sigma);
+                    statisticsFitnessHistory.add(bestFitness);
+                    statisticsMeanHistory.add(xmean.transpose());
+                    statisticsDHistory.add(diagD.transpose().scalarMultiply(1E5));
+                }
+            }
+        return optimum;
+    }
+
+    /**
+     * Checks dimensions and values of boundaries and inputSigma if defined.
+     */
+    private void checkParameters() {
+        double[] init = getStartPoint();
+        if (boundaries != null) {
+            if (boundaries.length != 2)
+                throw new MultiDimensionMismatchException(
+                        new Integer[] { boundaries.length },
+                        new Integer[] { 2 });
+            if (boundaries[0] == null || boundaries[1] == null)
+                throw new NoDataException();
+            if (boundaries[0].length != init.length)
+                throw new MultiDimensionMismatchException(
+                        new Integer[] { boundaries[0].length },
+                        new Integer[] { init.length });
+            if (boundaries[1].length != init.length)
+                throw new MultiDimensionMismatchException(
+                        new Integer[] { boundaries[1].length },
+                        new Integer[] { init.length });
+            for (int i = 0; i < init.length; i++) {
+                if (boundaries[0][i] > init[i] || boundaries[1][i] < init[i])
+                    throw new OutOfRangeException(init[i], boundaries[0][i],
+                            boundaries[1][i]);
+            }
+        }
+        if (inputSigma != null) {
+            if (inputSigma.length != init.length)
+                throw new MultiDimensionMismatchException(
+                        new Integer[] { inputSigma.length },
+                        new Integer[] { init.length });
+            for (int i = 0; i < init.length; i++) {
+                if (inputSigma[i] < 0)
+                    throw new NotPositiveException(inputSigma[i]);
+                if (boundaries != null) {
+                    if (inputSigma[i] > 1.0)
+                        throw new OutOfRangeException(inputSigma[i], 0, 1.0);
+                }
+            }
+        }
+    }
+
+    /**
+     * Initialization of the dynamic search parameters
+     *
+     * @param guess
+     *            initial guess for the arguments of the fitness function
+     */
+
+    private void initializeCMA(double[] guess) {
+        if (lambda <= 0)
+            lambda = 4 + (int) (3. * Math.log(dimension));
+        // initialize sigma
+        double[][] sigmaArray = new double[guess.length][1];
+        for (int i = 0; i < guess.length; i++)
+            sigmaArray[i][0] = inputSigma != null ? inputSigma[i] : 0.3;
+        RealMatrix insigma = new Array2DRowRealMatrix(sigmaArray, false);
+        sigma = max(insigma); // overall standard deviation
+
+        // initialize termination criteria
+        stopTolUpX = 1e3 * max(insigma);
+        stopTolX = 1e-11 * max(insigma);
+        stopTolFun = 1e-12;
+        stopTolHistFun = 1e-13;
+
+        // initialize selection strategy parameters
+        mu = lambda / 2; // number of parents/points for recombination
+        logMu2 = Math.log(mu + 0.5);
+        weights = log(sequence(1, mu, 1)).scalarMultiply(-1.).scalarAdd(logMu2);
+        double sumw = 0;
+        double sumwq = 0;
+        for (int i = 0; i < mu; i++) {
+            double w = weights.getEntry(i, 0);
+            sumw += w;
+            sumwq += w * w;
+        }
+        weights = weights.scalarMultiply(1. / sumw);
+        mueff = sumw * sumw / sumwq; // variance-effectiveness of sum w_i x_i
+
+        // initialize dynamic strategy parameters and constants
+        cc = (4. + mueff / dimension) /
+                (dimension + 4. + 2. * mueff / dimension);
+        cs = (mueff + 2.) / (dimension + mueff + 3.);
+        damps = (1. + 2. * Math.max(0, Math.sqrt((mueff - 1.) /
+                (dimension + 1.)) - 1.)) *
+                Math.max(0.3, 1. - dimension /
+                        (1e-6 + Math.min(maxIterations, getMaxEvaluations() /
+                                lambda))) + cs; // minor increment
+        ccov1 = 2. / ((dimension + 1.3) * (dimension + 1.3) + mueff);
+        ccovmu = Math.min(1 - ccov1, 2. * (mueff - 2. + 1. / mueff) /
+                ((dimension + 2.) * (dimension + 2.) + mueff));
+        ccov1Sep = Math.min(1, ccov1 * (dimension + 1.5) / 3.);
+        ccovmuSep = Math.min(1 - ccov1, ccovmu * (dimension + 1.5) / 3.);
+        chiN = Math.sqrt(dimension) *
+                (1. - 1. / (4. * dimension) + 1 / (21. * dimension * dimension));
+        // intialize CMA internal values - updated each generation
+        xmean = MatrixUtils.createColumnRealMatrix(guess); // objective
+                                                           // variables
+        diagD = insigma.scalarMultiply(1. / sigma);
+        diagC = square(diagD);
+        pc = zeros(dimension, 1); // evolution paths for C and sigma
+        ps = zeros(dimension, 1); // B defines the coordinate system
+        normps = norm(ps);
+
+        B = eye(dimension, dimension);
+        D = ones(dimension, 1); // diagonal D defines the scaling
+        BD = times(B, repmat(diagD.transpose(), dimension, 1));
+        C = B.multiply(diag(square(D)).multiply(B.transpose())); // covariance
+        historySize = 10 + (int) (3. * 10. * dimension / lambda);
+        fitnessHistory = new double[historySize]; // history of fitness values
+        for (int i = 0; i < historySize; i++)
+            fitnessHistory[i] = Double.MAX_VALUE;
+    }
+
+    /**
+     * Update of the evolution paths ps and pc
+     *
+     * @param zmean
+     *            weighted row matrix of the gaussian random numbers generating
+     *            the current offspring
+     * @param xold
+     *            xmean matrix of the previous generation
+     * @return hsig flag indicating a small correction
+     */
+    private boolean updateEvolutionPaths(RealMatrix zmean, RealMatrix xold) {
+        ps = ps.scalarMultiply(1. - cs).add(
+                B.multiply(zmean).scalarMultiply(
+                        Math.sqrt(cs * (2. - cs) * mueff)));
+        normps = norm(ps);
+        boolean hsig = normps /
+            Math.sqrt(1. - Math.pow(1. - cs, 2. * iterations)) /
+                chiN < 1.4 + 2. / (dimension + 1.);
+        pc = pc.scalarMultiply(1. - cc);
+        if (hsig)
+            pc = pc.add(xmean.subtract(xold).scalarMultiply(
+                    Math.sqrt(cc * (2. - cc) * mueff) / sigma));
+        return hsig;
+    }
+
+    /**
+     * Update of the covariance matrix C for diagonalOnly > 0
+     *
+     * @param hsig
+     *            flag indicating a small correction
+     * @param bestArz
+     *            fitness-sorted matrix of the gaussian random values of the
+     *            current offspring
+     * @param xold
+     *            xmean matrix of the previous generation
+     */
+    private void updateCovarianceDiagonalOnly(boolean hsig, final RealMatrix bestArz,
+            final RealMatrix xold) {
+        // minor correction if hsig==false
+        double oldFac = hsig ? 0 : ccov1Sep * cc * (2. - cc);
+        oldFac += 1. - ccov1Sep - ccovmuSep;
+        diagC = diagC.scalarMultiply(oldFac) // regard old matrix
+                // plus rank one update
+                .add(square(pc).scalarMultiply(ccov1Sep))
+                // plus rank mu update
+                .add((times(diagC, square(bestArz).multiply(weights)))
+                        .scalarMultiply(ccovmuSep));
+        diagD = sqrt(diagC); // replaces eig(C)
+        if (diagonalOnly > 1 && iterations > diagonalOnly) {
+            // full covariance matrix from now on
+            diagonalOnly = 0;
+            B = eye(dimension, dimension);
+            BD = diag(diagD);
+            C = diag(diagC);
+        }
+    }
+
+    /**
+     * Update of the covariance matrix C
+     *
+     * @param hsig
+     *            flag indicating a small correction
+     * @param bestArx
+     *            fitness-sorted matrix of the argument vectors producing the
+     *            current offspring
+     * @param arz
+     *            unsorted matrix containing the gaussian random values of the
+     *            current offspring
+     * @param arindex
+     *            indices indicating the fitness-order of the current offspring
+     * @param xold
+     *            xmean matrix of the previous generation
+     */
+    private void updateCovariance(boolean hsig, final RealMatrix bestArx,
+            final RealMatrix arz, final int[] arindex, final RealMatrix xold) {
+        double negccov = 0;
+        if (ccov1 + ccovmu > 0) {
+            RealMatrix arpos = bestArx.subtract(repmat(xold, 1, mu))
+                    .scalarMultiply(1. / sigma); // mu difference vectors
+            RealMatrix roneu = pc.multiply(pc.transpose())
+                    .scalarMultiply(ccov1); // rank one update
+            // minor correction if hsig==false
+            double oldFac = hsig ? 0 : ccov1 * cc * (2. - cc);
+            oldFac += 1. - ccov1 - ccovmu;
+            if (isActiveCMA) {
+                // Adapt covariance matrix C active CMA
+                negccov = (1. - ccovmu) * 0.25 * mueff /
+                (Math.pow(dimension + 2., 1.5) + 2. * mueff);
+                double negminresidualvariance = 0.66;
+                // keep at least 0.66 in all directions, small popsize are most
+                // critical
+                double negalphaold = 0.5; // where to make up for the variance
+                                          // loss,
+                // prepare vectors, compute negative updating matrix Cneg
+                int[] arReverseIndex = reverse(arindex);
+                RealMatrix arzneg = selectColumns(arz,
+                        Arrays.copyOf(arReverseIndex, mu));
+                RealMatrix arnorms = sqrt(sumRows(square(arzneg)));
+                int[] idxnorms = sortedIndices(arnorms.getRow(0));
+                RealMatrix arnormsSorted = selectColumns(arnorms, idxnorms);
+                int[] idxReverse = reverse(idxnorms);
+                RealMatrix arnormsReverse = selectColumns(arnorms, idxReverse);
+                arnorms = divide(arnormsReverse, arnormsSorted);
+                int[] idxInv = inverse(idxnorms);
+                RealMatrix arnormsInv = selectColumns(arnorms, idxInv);
+                // check and set learning rate negccov
+                double negcovMax = (1. - negminresidualvariance) /
+                        square(arnormsInv).multiply(weights).getEntry(0, 0);
+                if (negccov > negcovMax)
+                    negccov = negcovMax;
+                arzneg = times(arzneg, repmat(arnormsInv, dimension, 1));
+                RealMatrix artmp = BD.multiply(arzneg);
+                RealMatrix Cneg = artmp.multiply(diag(weights)).multiply(
+                        artmp.transpose());
+                oldFac += negalphaold * negccov;
+                C = C.scalarMultiply(oldFac)
+                        // regard old matrix
+                        .add(roneu)
+                        // plus rank one update
+                        .add(arpos.scalarMultiply(
+                                // plus rank mu update
+                                ccovmu + (1. - negalphaold) * negccov)
+                                .multiply(
+                                        times(repmat(weights, 1, dimension),
+                                                arpos.transpose())))
+                        .subtract(Cneg.scalarMultiply(negccov));
+            } else {
+                // Adapt covariance matrix C - nonactive
+                C = C.scalarMultiply(oldFac) // regard old matrix
+                        .add(roneu)
+                        // plus rank one update
+                        .add(arpos.scalarMultiply(ccovmu) // plus rank mu update
+                                .multiply(
+                                        times(repmat(weights, 1, dimension),
+                                                arpos.transpose())));
+            }
+        }
+        updateBD(negccov);
+    }
+
+    /**
+     * Update B and D from C
+     *
+     * @param negccov
+     *            Negative covariance factor.
+     */
+    private void updateBD(double negccov) {
+        if (ccov1 + ccovmu + negccov > 0 &&
+                (iterations % 1. / (ccov1 + ccovmu + negccov) / dimension / 10.) < 1.) {
+            // to achieve O(N^2)
+            C = triu(C, 0).add(triu(C, 1).transpose());
+            // enforce symmetry to prevent complex numbers
+            EigenDecomposition eig = new EigenDecompositionImpl(C, 1.0);
+            B = eig.getV(); // eigen decomposition, B==normalized eigenvectors
+            D = eig.getD();
+            diagD = diag(D);
+            if (min(diagD) <= 0) {
+                for (int i = 0; i < dimension; i++)
+                    if (diagD.getEntry(i, 0) < 0)
+                        diagD.setEntry(i, 0, 0.);
+                double tfac = max(diagD) / 1e14;
+                C = C.add(eye(dimension, dimension).scalarMultiply(tfac));
+                diagD = diagD.add(ones(dimension, 1).scalarMultiply(tfac));
+            }
+            if (max(diagD) > 1e14 * min(diagD)) {
+                double tfac = max(diagD) / 1e14 - min(diagD);
+                C = C.add(eye(dimension, dimension).scalarMultiply(tfac));
+                diagD = diagD.add(ones(dimension, 1).scalarMultiply(tfac));
+            }
+            diagC = diag(C);
+            diagD = sqrt(diagD); // D contains standard deviations now
+            BD = times(B, repmat(diagD.transpose(), dimension, 1)); // O(n^2)
+        }
+    }
+
+    /**
+     * Pushes the current best fitness value in a history queue.
+     *
+     * @param vals
+     *            the history queue
+     * @param val
+     *            current best fitness value
+     */
+    private static void push(double[] vals, double val) {
+        for (int i = vals.length-1; i > 0; i--)
+            vals[i] = vals[i-1];
+        vals[0] = val;
+    }
+
+    /**
+     * Sorts fitness values.
+     *
+     * @param doubles
+     *            array of values to be sorted
+     * @return sorted array of indices pointing into doubles
+     */
+    private int[] sortedIndices(final double[] doubles) {
+        DoubleIndex[] dis = new DoubleIndex[doubles.length];
+        for (int i = 0; i < doubles.length; i++)
+            dis[i] = new DoubleIndex(doubles[i], i);
+        Arrays.sort(dis);
+        int[] indices = new int[doubles.length];
+        for (int i = 0; i < doubles.length; i++)
+            indices[i] = dis[i].index;
+        return indices;
+    }
+
+    /**
+     * Used to sort fitness values. Sorting is always in lower value first
+     * order.
+     */
+    private static class DoubleIndex implements Comparable<DoubleIndex> {
+
+        /** Value to compare. */
+        private double value;
+        /** Index into sorted array. */
+        private int index;
+
+        /**
+         * @param value
+         *            Value to compare.
+         * @param index
+         *            Index into sorted array.
+         */
+        DoubleIndex(double value, int index) {
+            this.value = value;
+            this.index = index;
+        }
+
+        /** {@inheritDoc} */
+        public int compareTo(DoubleIndex o) {
+            return Double.compare(value, o.value);
+        }
+    }
+
+    /**
+     * Normalizes fitness values to the range [0,1]. Adds a penalty to the
+     * fitness value if out of range. The penalty is adjusted by calling
+     * setValueRange().
+     */
+    private class FitnessFunction {
+
+        /** Optional bounds for the objective variables */
+        private double[][] boundaries;
+        /** Determines the penalty for boundary violations */
+        private double valueRange = 1.0;
+        /**
+         * Flag indicating whether the objective variables are forced into their
+         * bounds if defined
+         */
+        private boolean isRepairMode = true;
+        /** Flag indicating the optimization goal. */
+        private boolean isMinimize = true;
+
+        /**
+         * @param boundaries
+         *            Bounds for the objective variables.
+         * @param isMinimize
+         *            Flag indicating the optimization goal.
+         */
+        private FitnessFunction(final double[][] boundaries,
+                final boolean isMinimize) {
+            this.boundaries = boundaries;
+            this.isMinimize = isMinimize;
+        }
+
+        /**
+         * @param x
+         *            Original objective variables.
+         * @return Normalized objective variables.
+         */
+        private double[] encode(final double[] x) {
+            if (boundaries == null)
+                return x;
+            double[] res = new double[x.length];
+            for (int i = 0; i < x.length; i++) {
+                double diff = boundaries[1][i] - boundaries[0][i];
+                res[i] = (x[i] - boundaries[0][i]) / diff;
+            }
+            return res;
+        }
+
+        /**
+         * @param x
+         *            Normalized objective variables.
+         * @return Original objective variables.
+         */
+        private double[] decode(final double[] x) {
+            if (boundaries == null)
+                return x;
+            double[] res = new double[x.length];
+            for (int i = 0; i < x.length; i++) {
+                double diff = boundaries[1][i] - boundaries[0][i];
+                res[i] = diff * x[i] + boundaries[0][i];
+            }
+            return res;
+        }
+
+        /**
+         * @param point
+         *            Normalized objective variables.
+         * @return Objective value + penalty for violated bounds.
+         */
+        private double value(final double[] point) {
+            double value;
+            if (boundaries != null && isRepairMode) {
+                double[] repaired = repair(point);
+                value = CMAESOptimizer.this
+                        .computeObjectiveValue(decode(repaired)) +
+                        penalty(point, repaired);
+            } else
+                value = CMAESOptimizer.this
+                        .computeObjectiveValue(decode(point));
+            return isMinimize ? value : -value;
+        }
+
+        /**
+         * @param x
+         *            Normalized objective variables.
+         * @return True if in bounds
+         */
+        private boolean isFeasible(final double[] x) {
+            if (boundaries == null)
+                return true;
+            for (int i = 0; i < x.length; i++) {
+                if (x[i] < 0)
+                    return false;
+                if (x[i] > 1.0)
+                    return false;
+            }
+            return true;
+        }
+
+        /**
+         * @param valueRange
+         *            Adjusts the penalty computation.
+         */
+        private void setValueRange(double valueRange) {
+            this.valueRange = valueRange;
+        }
+
+        /**
+         * @param x
+         *            Normalized objective variables.
+         * @return Repaired objective variables - all in bounds.
+         */
+        private double[] repair(final double[] x) {
+            double[] repaired = new double[x.length];
+            for (int i = 0; i < x.length; i++) {
+                if (x[i] < 0)
+                    repaired[i] = 0;
+                else if (x[i] > 1.0)
+                    repaired[i] = 1.0;
+                else
+                    repaired[i] = x[i];
+            }
+            return repaired;
+        }
+
+        /**
+         * @param x
+         *            Normalized objective variables.
+         * @param repaired
+         *            Repaired objective variables.
+         * @return Penalty value according to the violation of the bounds.
+         */
+        private double penalty(final double[] x, final double[] repaired) {
+            double penalty = 0;
+            for (int i = 0; i < x.length; i++) {
+                double diff = Math.abs(x[i] - repaired[i]);
+                penalty += diff * valueRange;
+            }
+            return isMinimize ? penalty : -penalty;
+        }
+    }
+
+    // -----Matrix utility functions similar to the Matlab build in functions------
+
+    /**
+     * @param m
+     *            Input matrix
+     * @return Matrix representing the element wise logarithm of m.
+     */
+    private static RealMatrix log(final RealMatrix m) {
+        double[][] d = new double[m.getRowDimension()][m.getColumnDimension()];
+        for (int r = 0; r < m.getRowDimension(); r++)
+            for (int c = 0; c < m.getColumnDimension(); c++)
+                d[r][c] = Math.log(m.getEntry(r, c));
+        return new Array2DRowRealMatrix(d, false);
+    }
+
+    /**
+     * @param m
+     *            Input matrix
+     * @return Matrix representing the element wise square root of m.
+     */
+    private static RealMatrix sqrt(final RealMatrix m) {
+        double[][] d = new double[m.getRowDimension()][m.getColumnDimension()];
+        for (int r = 0; r < m.getRowDimension(); r++)
+            for (int c = 0; c < m.getColumnDimension(); c++)
+                d[r][c] = Math.sqrt(m.getEntry(r, c));
+        return new Array2DRowRealMatrix(d, false);
+    }
+
+    /**
+     * @param m Input matrix
+     * @return Matrix representing the element wise square (^2) of m.
+     */
+    private static RealMatrix square(final RealMatrix m) {
+        double[][] d = new double[m.getRowDimension()][m.getColumnDimension()];
+        for (int r = 0; r < m.getRowDimension(); r++)
+            for (int c = 0; c < m.getColumnDimension(); c++) {
+                double e = m.getEntry(r, c);
+                d[r][c] = e * e;
+            }
+        return new Array2DRowRealMatrix(d, false);
+    }
+
+    /**
+     * @param m
+     *            Input matrix 1.
+     * @param n
+     *            Input matrix 2.
+     * @return Matrix where the elements of m and m are element wise multiplied.
+     */
+    private static RealMatrix times(final RealMatrix m, final RealMatrix n) {
+        double[][] d = new double[m.getRowDimension()][m.getColumnDimension()];
+        for (int r = 0; r < m.getRowDimension(); r++)
+            for (int c = 0; c < m.getColumnDimension(); c++)
+                d[r][c] = m.getEntry(r, c)*n.getEntry(r, c);
+        return new Array2DRowRealMatrix(d, false);
+    }
+
+    /**
+     * @param m
+     *            Input matrix 1.
+     * @param n
+     *            Input matrix 2.
+     * @return Matrix where the elements of m and m are element wise divided.
+     */
+    private static RealMatrix divide(final RealMatrix m, final RealMatrix n) {
+        double[][] d = new double[m.getRowDimension()][m.getColumnDimension()];
+        for (int r = 0; r < m.getRowDimension(); r++)
+            for (int c = 0; c < m.getColumnDimension(); c++)
+                d[r][c] = m.getEntry(r, c)/n.getEntry(r, c);
+        return new Array2DRowRealMatrix(d, false);
+    }
+
+    /**
+     * @param m Input matrix.
+     * @param cols Columns to select.
+     * @return Matrix representing the selected columns.
+     */
+    private static RealMatrix selectColumns(final RealMatrix m, final int[] cols) {
+        double[][] d = new double[m.getRowDimension()][cols.length];
+        for (int r = 0; r < m.getRowDimension(); r++)
+            for (int c = 0; c < cols.length; c++)
+                d[r][c] = m.getEntry(r, cols[c]);
+        return new Array2DRowRealMatrix(d, false);
+    }
+
+    /**
+     * @param m Input matrix.
+     * @param k diagonal position.
+     * @return Upper triangular part of matrix.
+     */
+    private static RealMatrix triu(final RealMatrix m, int k) {
+        double[][] d = new double[m.getRowDimension()][m.getColumnDimension()];
+        for (int r = 0; r < m.getRowDimension(); r++)
+            for (int c = 0; c < m.getColumnDimension(); c++)
+                d[r][c] = r <= c - k ? m.getEntry(r, c) : 0;
+                return new Array2DRowRealMatrix(d, false);
+    }
+
+    /**
+     * @param m
+     *            Input matrix.
+     * @return Norm of the matrix.
+     */
+    private static double norm(final RealMatrix m) {
+        double sum = 0;
+        for (int r = 0; r < m.getRowDimension(); r++)
+            for (int c = 0; c < m.getColumnDimension(); c++) {
+                double e = m.getEntry(r, c);
+                sum += e*e;
+            }
+        return Math.sqrt(sum);
+    }
+
+    /**
+     * @param m
+     *            Input matrix.
+     * @return Row matrix representing the sums of the rows.
+     */
+    private static RealMatrix sumRows(final RealMatrix m) {
+        double[][] d = new double[1][m.getColumnDimension()];
+        for (int c = 0; c < m.getColumnDimension(); c++) {
+            double sum = 0;
+            for (int r = 0; r < m.getRowDimension(); r++)
+                sum += m.getEntry(r, c);
+            d[0][c] = sum;
+        }
+        return new Array2DRowRealMatrix(d, false);
+    }
+
+    /**
+     * @param m
+     *            Input matrix.
+     * @return Diagonal n X n matrix if m is a column matrix, Rolumn matrix
+     *         representing the diagonal if m is a nXn matrix.
+     */
+    private static RealMatrix diag(final RealMatrix m) {
+        if (m.getColumnDimension() == 1) {
+            double[][] d = new double[m.getRowDimension()][m.getRowDimension()];
+            for (int i = 0; i < m.getRowDimension(); i++)
+                d[i][i] = m.getEntry(i, 0);
+            return new Array2DRowRealMatrix(d, false);
+        } else {
+            double[][] d = new double[m.getRowDimension()][1];
+            for (int i = 0; i < m.getColumnDimension(); i++)
+                d[i][0] = m.getEntry(i, i);
+            return new Array2DRowRealMatrix(d, false);
+        }
+    }
+
+    /**
+     * Copies a row from m1 to m2.
+     *
+     * @param m1
+     *            Source matrix 1.
+     * @param col1
+     *            Source column.
+     * @param m2
+     *            Target matrix.
+     * @param col2
+     *            Target column.
+     */
+    private static void copyColumn(final RealMatrix m1, int col1, RealMatrix m2, int col2) {
+        for (int i = 0; i < m1.getRowDimension(); i++)
+            m2.setEntry(i, col2, m1.getEntry(i, col1));
+    }
+
+    /**
+     * @param n
+     *            Number of rows.
+     * @param m
+     *            Number of columns.
+     * @return n X m matrix of 1.0-values.
+     */
+    private static RealMatrix ones(int n, int m) {
+        double[][] d = new double[n][m];
+        for (int r = 0; r < n; r++)
+            Arrays.fill(d[r], 1.0);
+        return new Array2DRowRealMatrix(d, false);
+    }
+
+    /**
+     * @param n
+     *            Number of rows.
+     * @param m
+     *            Number of columns.
+     * @return n X m matrix of 0.0-values, diagonal has values 1.0.
+     */
+    private static RealMatrix eye(int n, int m) {
+        double[][] d = new double[n][m];
+        for (int r = 0; r < n; r++)
+            if (r < m)
+                d[r][r] = 1;
+        return new Array2DRowRealMatrix(d, false);
+    }
+
+    /**
+     * @param n
+     *            Number of rows.
+     * @param m
+     *            Number of columns.
+     * @return n X m matrix of 0.0-values.
+     */
+    private static RealMatrix zeros(int n, int m) {
+        return new Array2DRowRealMatrix(n, m);
+    }
+
+    /**
+     * @param mat
+     *            Input matrix.
+     * @param n
+     *            Number of row replicates.
+     * @param m
+     *            Number of column replicates.
+     * @return Matrix which replicates the input matrix in both directions.
+     */
+    private static RealMatrix repmat(final RealMatrix mat, int n, int m) {
+        int rd = mat.getRowDimension();
+        int cd = mat.getColumnDimension();
+        double[][] d = new double[n * rd][m * cd];
+        for (int r = 0; r < n * rd; r++)
+            for (int c = 0; c < m * cd; c++)
+                d[r][c] = mat.getEntry(r % rd, c % cd);
+        return new Array2DRowRealMatrix(d, false);
+    }
+
+    /**
+     * @param start
+     *            Start value.
+     * @param end
+     *            End value.
+     * @param step
+     *            Step size.
+     * @return Sequence as column matrix.
+     */
+    private static RealMatrix sequence(double start, double end, double step) {
+        int size = (int) ((end - start) / step + 1);
+        double[][] d = new double[size][1];
+        double value = start;
+        for (int r = 0; r < size; r++) {
+            d[r][0] = value;
+            value += step;
+        }
+        return new Array2DRowRealMatrix(d, false);
+    }
+
+    /**
+     * @param m
+     *            Input matrix.
+     * @return Maximum of matrix element values.
+     */
+    private static double max(final RealMatrix m) {
+        double max = -Double.MAX_VALUE;
+        for (int r = 0; r < m.getRowDimension(); r++)
+            for (int c = 0; c < m.getColumnDimension(); c++) {
+                double e = m.getEntry(r, c);
+                if (max < e)
+                    max = e;
+            }
+        return max;
+    }
+
+    /**
+     * @param m
+     *            Input matrix.
+     * @return Minimum of matrix element values.
+     */
+    private static double min(final RealMatrix m) {
+        double min = Double.MAX_VALUE;
+        for (int r = 0; r < m.getRowDimension(); r++)
+            for (int c = 0; c < m.getColumnDimension(); c++) {
+                double e = m.getEntry(r, c);
+                if (min > e)
+                    min = e;
+            }
+        return min;
+    }
+
+    /**
+     * @param m
+     *            Input array.
+     * @return Maximum of array values.
+     */
+    private static double max(final double[] m) {
+        double max = -Double.MAX_VALUE;
+        for (int r = 0; r < m.length; r++)
+            if (max < m[r])
+                max = m[r];
+        return max;
+    }
+
+    /**
+     * @param m
+     *            Input array.
+     * @return Minimum of array values.
+     */
+    private static double min(final double[] m) {
+        double min = Double.MAX_VALUE;
+        for (int r = 0; r < m.length; r++)
+            if (min > m[r])
+                min = m[r];
+        return min;
+    }
+
+    /**
+     * @param indices
+     *            Input index array.
+     * @return Inverse of the mapping defined by indices
+     */
+    private static int[] inverse(final int[] indices) {
+        int[] inverse = new int[indices.length];
+        for (int i = 0; i < indices.length; i++)
+            inverse[indices[i]] = i;
+        return inverse;
+    }
+
+    /**
+     * @param indices
+     *            Input index array.
+     * @return Indices in inverse order (last is first)
+     */
+    private static int[] reverse(final int[] indices) {
+        int[] reverse = new int[indices.length];
+        for (int i = 0; i < indices.length; i++)
+            reverse[i] = indices[indices.length - i - 1];
+        return reverse;
+    }
+
+    /**
+     * @param size
+     *            Length of random array.
+     * @return Array of gaussian random numbers.
+     */
+    private double[] randn(int size) {
+        double[] randn = new double[size];
+        for (int i = 0; i < size; i++)
+            randn[i] = random.nextGaussian();
+        return randn;
+    }
+
+    /**
+     * @param size
+     *            Number of rows.
+     * @param popSize
+     *            Population size.
+     * @return 2-dimensional matrix of gaussian random numbers.
+     */
+    private RealMatrix randn1(int size, int popSize) {
+        double[][] d = new double[size][popSize];
+        for (int r = 0; r < size; r++)
+            for (int c = 0; c < popSize; c++)
+                d[r][c] = random.nextGaussian();
+        return new Array2DRowRealMatrix(d, false);
+    }
+}
+

Propchange: commons/proper/math/trunk/src/main/java/org/apache/commons/math/optimization/direct/CMAESOptimizer.java
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    svn:eol-style = native

Added: commons/proper/math/trunk/src/test/java/org/apache/commons/math/optimization/direct/CMAESOptimizerTest.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/java/org/apache/commons/math/optimization/direct/CMAESOptimizerTest.java?rev=1067216&view=auto
==============================================================================
--- commons/proper/math/trunk/src/test/java/org/apache/commons/math/optimization/direct/CMAESOptimizerTest.java (added)
+++ commons/proper/math/trunk/src/test/java/org/apache/commons/math/optimization/direct/CMAESOptimizerTest.java Fri Feb  4 16:36:08 2011
@@ -0,0 +1,667 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math.optimization.direct;
+
+import java.util.Arrays;
+import java.util.Random;
+
+import org.apache.commons.math.MathException;
+import org.apache.commons.math.analysis.MultivariateRealFunction;
+import org.apache.commons.math.exception.MathUserException;
+import org.apache.commons.math.exception.MultiDimensionMismatchException;
+import org.apache.commons.math.exception.NoDataException;
+import org.apache.commons.math.exception.NotPositiveException;
+import org.apache.commons.math.exception.OutOfRangeException;
+import org.apache.commons.math.optimization.GoalType;
+import org.apache.commons.math.optimization.MultivariateRealOptimizer;
+import org.apache.commons.math.optimization.RealPointValuePair;
+import org.apache.commons.math.random.MersenneTwister;
+import org.junit.Assert;
+import org.junit.Test;
+
+/**
+ * Test for {@link CMAESOptimizer}.
+ */
+public class CMAESOptimizerTest {
+
+    static final int DIM = 13;
+    static final int LAMBDA = 4 + (int)(3.*Math.log(DIM));
+   
+    @Test(expected = OutOfRangeException.class)
+    public void testInitOutofbounds() throws MathUserException, MathException {
+        double[] startPoint = point(DIM,3);
+        double[] insigma = null;
+        double[][] boundaries = boundaries(DIM,-1,2);
+        RealPointValuePair expected =
+            new RealPointValuePair(point(DIM,1.0),0.0);
+        doTest(new Rosen(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
+                1e-13, 1e-6, 100000, expected);
+    }
+    
+    @Test(expected = MultiDimensionMismatchException.class)
+    public void testBoundariesDimensionMismatch() throws MathUserException, MathException {
+        double[] startPoint = point(DIM,0.5);
+        double[] insigma = null;
+        double[][] boundaries = boundaries(DIM+1,-1,2);
+        RealPointValuePair expected =
+            new RealPointValuePair(point(DIM,1.0),0.0);
+        doTest(new Rosen(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
+                1e-13, 1e-6, 100000, expected);
+    }
+
+    @Test(expected = NoDataException.class)
+    public void testBoundariesNoData() throws MathUserException, MathException {
+        double[] startPoint = point(DIM,0.5);
+        double[] insigma = null;
+        double[][] boundaries = boundaries(DIM,-1,2);
+        boundaries[1] = null;
+        RealPointValuePair expected =
+            new RealPointValuePair(point(DIM,1.0),0.0);
+        doTest(new Rosen(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
+                1e-13, 1e-6, 100000, expected);
+    }
+
+    @Test(expected = NotPositiveException.class)
+    public void testInputSigmaNegative() throws MathUserException, MathException {
+        double[] startPoint = point(DIM,0.5);
+        double[] insigma = point(DIM,-0.5);
+        double[][] boundaries = null;
+        RealPointValuePair expected =
+            new RealPointValuePair(point(DIM,1.0),0.0);
+        doTest(new Rosen(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
+                1e-13, 1e-6, 100000, expected);
+    }
+
+    @Test(expected = OutOfRangeException.class)
+    public void testInputSigmaOutOfRange() throws MathUserException, MathException {
+        double[] startPoint = point(DIM,0.5);
+        double[] insigma = point(DIM, 1.1);
+        double[][] boundaries = boundaries(DIM,-1,2);
+        RealPointValuePair expected =
+            new RealPointValuePair(point(DIM,1.0),0.0);
+        doTest(new Rosen(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
+                1e-13, 1e-6, 100000, expected);
+    }
+
+    @Test(expected = MultiDimensionMismatchException.class)
+    public void testInputSigmaDimensionMismatch() throws MathUserException, MathException {
+        double[] startPoint = point(DIM,0.5);
+        double[] insigma = point(DIM+1,-0.5);
+        double[][] boundaries = null;;
+        RealPointValuePair expected =
+            new RealPointValuePair(point(DIM,1.0),0.0);
+        doTest(new Rosen(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
+                1e-13, 1e-6, 100000, expected);
+    }
+    
+    @Test
+    public void testRosen() throws MathException {
+        double[] startPoint = point(DIM,0.1);
+        double[] insigma = point(DIM,0.1);
+        double[][] boundaries = null;
+        RealPointValuePair expected =
+            new RealPointValuePair(point(DIM,1.0),0.0);
+        doTest(new Rosen(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
+                1e-13, 1e-6, 100000, expected);
+        doTest(new Rosen(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, LAMBDA, false, 0, 1e-13,
+                1e-13, 1e-6, 100000, expected);
+    }
+
+    @Test
+    public void testMaximize() throws MathException {
+        double[] startPoint = point(DIM,1.0);
+        double[] insigma = point(DIM,0.1);
+        double[][] boundaries = null;
+        RealPointValuePair expected =
+            new RealPointValuePair(point(DIM,0.0),1.0);
+        doTest(new MinusElli(), startPoint, insigma, boundaries,
+                GoalType.MAXIMIZE, LAMBDA, true, 0, 1.0-1e-13,
+                2e-10, 5e-6, 100000, expected);
+        doTest(new MinusElli(), startPoint, insigma, boundaries,
+                GoalType.MAXIMIZE, LAMBDA, false, 0, 1.0-1e-13,
+                2e-10, 5e-6, 100000, expected);
+        boundaries = boundaries(DIM,-0.3,0.3); 
+        startPoint = point(DIM,0.1);
+        doTest(new MinusElli(), startPoint, insigma, boundaries,
+                GoalType.MAXIMIZE, LAMBDA, true, 0, 1.0-1e-13,
+                2e-10, 5e-6, 100000, expected);
+    }
+
+    @Test
+    public void testEllipse() throws MathException {
+        double[] startPoint = point(DIM,1.0);
+        double[] insigma = point(DIM,0.1);
+        double[][] boundaries = null;
+        RealPointValuePair expected =
+            new RealPointValuePair(point(DIM,0.0),0.0);
+        doTest(new Elli(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
+                1e-13, 1e-6, 100000, expected);
+        doTest(new Elli(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, LAMBDA, false, 0, 1e-13,
+                1e-13, 1e-6, 100000, expected);
+    }
+
+    @Test
+    public void testElliRotated() throws MathException {
+        double[] startPoint = point(DIM,1.0);
+        double[] insigma = point(DIM,0.1);
+        double[][] boundaries = null;
+        RealPointValuePair expected =
+            new RealPointValuePair(point(DIM,0.0),0.0);
+        doTest(new ElliRotated(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
+                1e-13, 1e-6, 100000, expected);
+        doTest(new ElliRotated(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, LAMBDA, false, 0, 1e-13,
+                1e-13, 1e-6, 100000, expected);
+    }
+
+    @Test
+    public void testCigar() throws MathException {
+        double[] startPoint = point(DIM,1.0);
+        double[] insigma = point(DIM,0.1);
+        double[][] boundaries = null;
+        RealPointValuePair expected =
+            new RealPointValuePair(point(DIM,0.0),0.0);
+        doTest(new Cigar(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
+                1e-13, 1e-6, 200000, expected);
+        doTest(new Cigar(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, LAMBDA, false, 0, 1e-13,
+                1e-13, 1e-6, 100000, expected);
+    }
+
+    @Test
+    public void testTwoAxes() throws MathException {
+        double[] startPoint = point(DIM,1.0);
+        double[] insigma = point(DIM,0.1);
+        double[][] boundaries = null;
+        RealPointValuePair expected =
+            new RealPointValuePair(point(DIM,0.0),0.0);
+        doTest(new TwoAxes(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, 2*LAMBDA, true, 0, 1e-13,
+                1e-13, 1e-6, 200000, expected);
+        doTest(new TwoAxes(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, 2*LAMBDA, false, 0, 1e-13,
+                1e-8, 1e-3, 200000, expected);
+    }
+
+    @Test
+    public void testCigTab() throws MathException {
+        double[] startPoint = point(DIM,1.0);
+        double[] insigma = point(DIM,0.3);
+        double[][] boundaries = null;
+        RealPointValuePair expected =
+            new RealPointValuePair(point(DIM,0.0),0.0);
+        doTest(new CigTab(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
+                1e-13, 5e-5, 100000, expected);
+        doTest(new CigTab(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, LAMBDA, false, 0, 1e-13,
+                1e-13, 5e-5, 100000, expected);
+    }
+
+    @Test
+    public void testSphere() throws MathException {
+        double[] startPoint = point(DIM,1.0);
+        double[] insigma = point(DIM,0.1);
+        double[][] boundaries = null;
+        RealPointValuePair expected =
+            new RealPointValuePair(point(DIM,0.0),0.0);
+        doTest(new Sphere(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
+                1e-13, 1e-6, 100000, expected);
+        doTest(new Sphere(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, LAMBDA, false, 0, 1e-13,
+                1e-13, 1e-6, 100000, expected);
+    }
+
+    @Test
+    public void testTablet() throws MathException {
+        double[] startPoint = point(DIM,1.0);
+        double[] insigma = point(DIM,0.1);
+        double[][] boundaries = null;
+        RealPointValuePair expected =
+            new RealPointValuePair(point(DIM,0.0),0.0);
+        doTest(new Tablet(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
+                1e-13, 1e-6, 100000, expected);
+        doTest(new Tablet(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, LAMBDA, false, 0, 1e-13,
+                1e-13, 1e-6, 100000, expected);
+    }
+
+    @Test
+    public void testDiffPow() throws MathException {
+        double[] startPoint = point(DIM,1.0);
+        double[] insigma = point(DIM,0.1);
+        double[][] boundaries = null;
+        RealPointValuePair expected =
+            new RealPointValuePair(point(DIM,0.0),0.0);
+        doTest(new DiffPow(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, 10, true, 0, 1e-13,
+                1e-8, 1e-1, 100000, expected);
+        doTest(new DiffPow(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, 10, false, 0, 1e-13,
+                1e-8, 2e-1, 100000, expected);
+    }
+
+    @Test
+    public void testSsDiffPow() throws MathException {
+        double[] startPoint = point(DIM,1.0);
+        double[] insigma = point(DIM,0.1);
+        double[][] boundaries = null;
+        RealPointValuePair expected =
+            new RealPointValuePair(point(DIM,0.0),0.0);
+        doTest(new SsDiffPow(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, 10, true, 0, 1e-13,
+                1e-4, 1e-1, 200000, expected);
+        doTest(new SsDiffPow(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, 10, false, 0, 1e-13,
+                1e-4, 1e-1, 200000, expected);
+    }
+
+    @Test
+    public void testAckley() throws MathException {
+        double[] startPoint = point(DIM,1.0);
+        double[] insigma = point(DIM,1.0);
+        double[][] boundaries = null;
+        RealPointValuePair expected =
+            new RealPointValuePair(point(DIM,0.0),0.0);
+        doTest(new Ackley(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, 2*LAMBDA, true, 0, 1e-13,
+                1e-9, 1e-5, 100000, expected);
+        doTest(new Ackley(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, 2*LAMBDA, false, 0, 1e-13,
+                1e-9, 1e-5, 100000, expected);
+    }
+
+    @Test
+    public void testRastrigin() throws MathException {
+        double[] startPoint = point(DIM,0.1);
+        double[] insigma = point(DIM,0.1);
+        double[][] boundaries = null;
+        RealPointValuePair expected =
+            new RealPointValuePair(point(DIM,0.0),0.0);
+        doTest(new Rastrigin(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, (int)(200*Math.sqrt(DIM)), true, 0, 1e-13,
+                1e-13, 1e-6, 200000, expected);
+        doTest(new Rastrigin(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, (int)(200*Math.sqrt(DIM)), false, 0, 1e-13,
+                1e-13, 1e-6, 200000, expected);
+    }
+
+    @Test
+    public void testConstrainedRosen() throws MathException {
+        double[] startPoint = point(DIM,0.1);
+        double[] insigma = point(DIM,0.1);
+        double[][] boundaries = boundaries(DIM,-1,2);
+        RealPointValuePair expected =
+            new RealPointValuePair(point(DIM,1.0),0.0);
+        doTest(new Rosen(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, 2*LAMBDA, true, 0, 1e-13,
+                1e-13, 1e-6, 100000, expected);
+        doTest(new Rosen(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, 2*LAMBDA, false, 0, 1e-13,
+                1e-13, 1e-6, 100000, expected);
+    }
+
+    @Test
+    public void testDiagonalRosen() throws MathException {
+        double[] startPoint = point(DIM,0.1);
+        double[] insigma = point(DIM,0.1);
+        double[][] boundaries = null;
+        RealPointValuePair expected =
+            new RealPointValuePair(point(DIM,1.0),0.0);
+        doTest(new Rosen(), startPoint, insigma, boundaries,
+                GoalType.MINIMIZE, LAMBDA, false, 1, 1e-13,
+                1e-10, 1e-4, 1000000, expected);
+     }
+
+    /**
+     * @param func Function to optimize.
+     * @param startPoint Starting point.
+     * @param inSigma Individual input sigma.
+     * @param boundaries Upper / lower point limit.
+     * @param goal Minimization or maximization.
+     * @param lambda Population size used for offspring.
+     * @param isActive Covariance update mechanism.
+     * @param diagonalOnly Simplified covariance update.
+     * @param stopValue Termination criteria for optimization.
+     * @param fTol Tolerance relative error on the objective function.
+     * @param pointTol Tolerance for checking that the optimum is correct.
+     * @param maxEvaluations Maximum number of evaluations.
+     * @param expected Expected point / value.
+     */
+    private void doTest(MultivariateRealFunction func,
+            double[] startPoint,
+            double[] inSigma,
+            double[][] boundaries,
+            GoalType goal,
+            int lambda,
+            boolean isActive,
+            int diagonalOnly, 
+            double stopValue,
+            double fTol,
+            double pointTol,
+            int maxEvaluations,
+            RealPointValuePair expected)
+    throws MathException {
+        int dim = startPoint.length;
+        // test diagonalOnly = 0 - slow but normally fewer feval#
+        MultivariateRealOptimizer optim =
+            new CMAESOptimizer(
+                    lambda, inSigma, boundaries, 30000,
+                    stopValue, isActive, diagonalOnly, 0, new MersenneTwister(),false);
+        RealPointValuePair result = optim.optimize(maxEvaluations, func, goal, startPoint);
+        Assert.assertEquals(expected.getValue(),
+                result.getValue(), fTol);
+        for (int i = 0; i < dim; i++) {
+            Assert.assertEquals(expected.getPoint()[i],
+                    result.getPoint()[i], pointTol);
+        }
+    }
+
+    private static double[] point(int n, double value) {
+        double[] ds = new double[n];
+        Arrays.fill(ds, value);
+        return ds;
+    }
+
+    private static double[][] boundaries(int dim,
+            double lower, double upper) {
+        double[][] boundaries = new double[2][dim];
+        for (int i = 0; i < dim; i++)
+            boundaries[0][i] = lower;
+        for (int i = 0; i < dim; i++)
+            boundaries[1][i] = upper;
+        return boundaries;
+    }
+
+    private static class Sphere implements MultivariateRealFunction {
+
+        public double value(double[] x) {
+            double f = 0;
+            for (int i = 0; i < x.length; ++i)
+                f += x[i] * x[i];
+            return f;
+        }
+    }
+
+    private static class Cigar implements MultivariateRealFunction {
+        private double factor;
+
+        Cigar() {
+            this(1e3);
+        }
+
+        Cigar(double axisratio) {
+            factor = axisratio * axisratio;
+        }
+
+        public double value(double[] x) {
+            double f = x[0] * x[0];
+            for (int i = 1; i < x.length; ++i)
+                f += factor * x[i] * x[i];
+            return f;
+        }
+    }
+
+    private static class Tablet implements MultivariateRealFunction {
+        private double factor;
+
+        Tablet() {
+            this(1e3);
+        }
+
+        Tablet(double axisratio) {
+            factor = axisratio * axisratio;
+        }
+
+        public double value(double[] x) {
+            double f = factor * x[0] * x[0];
+            for (int i = 1; i < x.length; ++i)
+                f += x[i] * x[i];
+            return f;
+        }
+    }
+
+    private static class CigTab implements MultivariateRealFunction {
+        private double factor;
+
+        CigTab() {
+            this(1e4);
+        }
+
+        CigTab(double axisratio) {
+            factor = axisratio;
+        }
+
+        public double value(double[] x) {
+            int end = x.length - 1;
+            double f = x[0] * x[0] / factor + factor * x[end] * x[end];
+            for (int i = 1; i < end; ++i)
+                f += x[i] * x[i];
+            return f;
+        }
+    }
+
+    private static class TwoAxes implements MultivariateRealFunction {
+
+        private double factor;
+
+        TwoAxes() {
+            this(1e6);
+        }
+
+        TwoAxes(double axisratio) {
+            factor = axisratio * axisratio;
+        }
+
+        public double value(double[] x) {
+            double f = 0;
+            for (int i = 0; i < x.length; ++i)
+                f += (i < x.length / 2 ? factor : 1) * x[i] * x[i];
+            return f;
+        }
+    }
+
+    private static class ElliRotated implements MultivariateRealFunction {
+        private Basis B = new Basis();
+        private double factor;
+
+        ElliRotated() {
+            this(1e3);
+        }
+
+        ElliRotated(double axisratio) {
+            factor = axisratio * axisratio;
+        }
+
+        public double value(double[] x) {
+            double f = 0;
+            x = B.Rotate(x);
+            for (int i = 0; i < x.length; ++i)
+                f += Math.pow(factor, i / (x.length - 1.)) * x[i] * x[i];
+            return f;
+        }
+    }
+
+    private static class Elli implements MultivariateRealFunction {
+
+        private double factor;
+
+        Elli() {
+            this(1e3);
+        }
+
+        Elli(double axisratio) {
+            factor = axisratio * axisratio;
+        }
+
+        public double value(double[] x) {
+            double f = 0;
+            for (int i = 0; i < x.length; ++i)
+                f += Math.pow(factor, i / (x.length - 1.)) * x[i] * x[i];
+            return f;
+        }
+    }
+
+    private static class MinusElli implements MultivariateRealFunction {
+
+        public double value(double[] x) {
+            return 1.0-(new Elli().value(x));
+        }
+    }
+
+    private static class DiffPow implements MultivariateRealFunction {
+
+        public double value(double[] x) {
+            double f = 0;
+            for (int i = 0; i < x.length; ++i)
+                f += Math.pow(Math.abs(x[i]), 2. + 10 * (double) i
+                        / (x.length - 1.));
+            return f;
+        }
+    }
+
+    private static class SsDiffPow implements MultivariateRealFunction {
+
+        public double value(double[] x) {
+            double f = Math.pow(new DiffPow().value(x), 0.25);
+            return f;
+        }
+    }
+
+    private static class Rosen implements MultivariateRealFunction {
+
+        public double value(double[] x) {
+            double f = 0;
+            for (int i = 0; i < x.length - 1; ++i)
+                f += 1e2 * (x[i] * x[i] - x[i + 1]) * (x[i] * x[i] - x[i + 1])
+                + (x[i] - 1.) * (x[i] - 1.);
+            return f;
+        }
+    }
+
+    private static class Ackley implements MultivariateRealFunction {
+        private double axisratio;
+
+        Ackley(double axra) {
+            axisratio = axra;
+        }
+
+        public Ackley() {
+            this(1);
+        }
+
+        public double value(double[] x) {
+            double f = 0;
+            double res2 = 0;
+            double fac = 0;
+            for (int i = 0; i < x.length; ++i) {
+                fac = Math.pow(axisratio, (i - 1.) / (x.length - 1.));
+                f += fac * fac * x[i] * x[i];
+                res2 += Math.cos(2. * Math.PI * fac * x[i]);
+            }
+            f = (20. - 20. * Math.exp(-0.2 * Math.sqrt(f / x.length))
+                    + Math.exp(1.) - Math.exp(res2 / x.length));
+            return f;
+        }
+    }
+
+    private static class Rastrigin implements MultivariateRealFunction {
+
+        private double axisratio;
+        private double amplitude;
+
+        Rastrigin() {
+            this(1, 10);
+        }
+
+        Rastrigin(double axisratio, double amplitude) {
+            this.axisratio = axisratio;
+            this.amplitude = amplitude;
+        }
+
+        public double value(double[] x) {
+            double f = 0;
+            double fac;
+            for (int i = 0; i < x.length; ++i) {
+                fac = Math.pow(axisratio, (i - 1.) / (x.length - 1.));
+                if (i == 0 && x[i] < 0)
+                    fac *= 1.;
+                f += fac * fac * x[i] * x[i] + amplitude
+                * (1. - Math.cos(2. * Math.PI * fac * x[i]));
+            }
+            return f;
+        }
+    }
+
+    private static class Basis {
+        double[][] basis;
+        Random rand = new Random(2); // use not always the same basis
+
+        double[] Rotate(double[] x) {
+            GenBasis(x.length);
+            double[] y = new double[x.length];
+            for (int i = 0; i < x.length; ++i) {
+                y[i] = 0;
+                for (int j = 0; j < x.length; ++j)
+                    y[i] += basis[i][j] * x[j];
+            }
+            return y;
+        }
+
+        void GenBasis(int DIM) {
+            if (basis != null ? basis.length == DIM : false)
+                return;
+
+            double sp;
+            int i, j, k;
+
+            /* generate orthogonal basis */
+            basis = new double[DIM][DIM];
+            for (i = 0; i < DIM; ++i) {
+                /* sample components gaussian */
+                for (j = 0; j < DIM; ++j)
+                    basis[i][j] = rand.nextGaussian();
+                /* substract projection of previous vectors */
+                for (j = i - 1; j >= 0; --j) {
+                    for (sp = 0., k = 0; k < DIM; ++k)
+                        sp += basis[i][k] * basis[j][k]; /* scalar product */
+                    for (k = 0; k < DIM; ++k)
+                        basis[i][k] -= sp * basis[j][k]; /* substract */
+                }
+                /* normalize */
+                for (sp = 0., k = 0; k < DIM; ++k)
+                    sp += basis[i][k] * basis[i][k]; /* squared norm */
+                for (k = 0; k < DIM; ++k)
+                    basis[i][k] /= Math.sqrt(sp);
+            }
+        }
+    }
+}

Propchange: commons/proper/math/trunk/src/test/java/org/apache/commons/math/optimization/direct/CMAESOptimizerTest.java
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